Mechanism of Interaction of Water above the Methylammonium Lead Iodide Perovskite Nanocluster: Size Effect and Water-Induced Defective States

Water is often viewed as detrimental to organic halide perovskite stability. However, evidence highlights its efficacy as a solvent during organic perovskite liquid synthesis. This paradox prompts an investigation into water’s influence on perovskite nanoclusters. Employing first principle calculations and ab initio molecular dynamics simulations, surprisingly, we discover some subsurface layers of methylammonium lead iodide (MAPbI3) nanoclusters exhibit stronger relaxation than surface layers. Moreover, a strong quantum confinement effect enhances the band gap of MAPbI3 as the nanocluster size decreases. Notably, the water molecules above MAPbI3 nanoclusters induce rich localized defect states, generating low-lying shallow states above the valence band for the small amounts of surface water molecules and band-like deep states across the whole gap for large nanoclusters. This work provides insights into water’s role in the electronic structure and structural evolution of perovskite nanoclusters, aiding the design of water-resistant layers to protect perovskite quantum dots from ambient humidity.


Adsorption energy calculation details
Table S1: The energies, calculated in Atomic Units (a.u.), are used to determine adsorption energies for three systems employing the CP2K parameters EPS SCF set to 1.0E-6 and MAX SCF set to 150.These energies include (i).E total , which is computed from the relaxed configuration of the nanocluster and water; (ii).E cluster , calculated from the relaxed configuration with surrounding water molecules removed; and (iii).E water , determined from the relaxed configuration with the central MAPbI 3 cluster removed.The adsorption energy E adsorb is derived using the formula E adsorb = E total − E cluster − E water .

Perovskite-water ratio impact on the MAPbI 3 cluster
To explore the evolution of structure and electronic properties in MAPbI 3 clusters as the perovskite-water ratio increases, we focused on a small MAPbI 3 nanocluster as a representative example.We systematically reduced the number of surrounding water molecules, performing structure optimizations for each system.The initial structures, depicted in Figure S1 (a2)-(g2), were constructed with water molecules positioned on the lattice, as illustrated in Figure S1 (a1)-(g1), where red dots denote the sites for oxygen atoms.
The systems (a) to (g) exhibit a gradual reduction in the number of water molecules, ranging from 156 to 0. For specific details on the number of water molecules in each system, please refer to Table S2.In Figure S1, columns 3 and 4 present the relaxed structures, with and without the surrounding water molecules, respectively.The latter representation aims to facilitate a clearer observation of structural changes in the central MAPbI 3 clusters.) investigate electronic properties.For system details, refer to Table S2.

Structural impact of water presence
In comparison to the absence of water molecules in the surrounding environment (g), the introduction of water proves beneficial in maintaining the crystalline structure of MAPbI 3 to some extent, even in the case of a minimal amount of water molecules, as observed in system (f).To quantitatively assess the deviation between the relaxed and initial MAPbI 3 structures, we calculate the cosine similarity for each cluster using the formula: where S(X 0 , X t ) quantifies the similarity between two high-dimensional vectors X at time 0 and time t, encompassing all atom coordinates within the nanocluster.
As shown in Table S2, system (g), with no water molecules surrounding the central MAPbI 3 cluster, exhibits the lowest similarity, indicating the most significant structural change compared to other systems with surrounding water molecules.Intriguingly, system (f), with a minimal amount of water molecules, demonstrates the highest similarity, suggesting that system (f) preserved the best crystal structure.In other words, the influence of water molecules on stabilizing MAPbI 3 does not exhibit a gradual characteristic as their quantity increases.S2 (a) and (b) depict structures at different optimization stages for systems (g) (no water molecules) and (f) (39 water molecules), respectively.In (a), the MAPbI 3 cluster in system (g) loses its octahedral structure gradually, while in (b), the basic crystal structure of the MAPbI 3 cluster in system (f) with a small amount of water molecules remains preserved.This observation aligns with findings from previous works, [1][2][3] highlighting the stabilizing role of a small quantity of water molecules in the MAPbI 3 crystal structure.

Electronic property impact of water presence
To investigate the impact of the perovskite-water ratio on the electronic properties of these systems, we conducted projected density of states (PDOS) calculations for both the bare clusters (Figure S1, column 4) and the cluster-water systems (Figure S1, column 3), presented in column 5 and 6 of Figure S1, respectively.Band gaps for the bare MAPbI 3 clusters in all systems are plotted and detailed in Table S2.
The band gaps for naked nanoclusters range from 2.23 eV to 2.57 eV, excluding system (g) without surrounding water molecules, where defective states, primarily comprised of iodine, form within the band gap of MAPbI 3 .Examining the PDOS calculations in Figure S1 (a6-f6) with water molecules, defective states are observed in all systems, with oxygen and iodine atoms contributing the most.

AIMD trajectory analysis
3.1 The evolution of MAPbI 3 structure In Figure S3, we analyzed the progression of structural similarity over time in the nanocluster.
We also included the nanocluster in bulk water for comparison.The results showed significant changes in structural similarity within the first 2 ps, followed by a relatively slower rate of change.Cosine similarity S(X 0 , X t )

Water layer Bulk water
Figure S3: Snapshots of the small nanocluster configurations at water layer and bulk water environments within the first 4 ps, as obtained from AIMD trajectories.Additionally, the corresponding cosine similarity as a function of time is also plotted.

The evolution of coordination numbers
The RDF g αβ (r) measures the averaged particle β density as a function of distance from a central atom α and is calculated by where n(r) is the atom β number between r and r + ∆r, ρ is the number density of atom β.
The coordination number CN αβ is used to describe the number of neighbors β surrounding a reference atom α within a system and is given by where r ′ denotes the cutoff distance, representing the radial extent within which neighboring entities are considered.Here, the first minimum of the RDF is chosen as r ′ .

Figure S1 :
Figure S1: Evolution of MAPbI 3 Clusters: Investigating structural and PDOS changes with varying perovskite-water ratios.The figure illustrates the progressive reduction of water molecules, as depicted from (a2) to (g2).The surrounding water molecules are placed in ways as shown from (a1) to (g1), where red dots denote oxygen atom positions.The systems exhibit decreasing water molecules from 156 to 0. Relaxed structures with/without water molecules (columns 3 and 4) highlight changes in the central MAPbI 3 clusters.PDOS calculations (columns 5 and 6) investigate electronic properties.For system details, refer to TableS2.

Figure S2 :
Figure S2: Structural optimization processes for (a) the naked cluster system (g) without surrounding water molecules and (b) the system (f) with 39 water molecules.In (b), water molecules are not plotted for clearer comparison.Due to differing optimization steps (240 for (a) and 361 for (b)), configurations at equivalent percentages of optimization processes are depicted.In (a), the naked nanocluster gradually loses its octahedral structure during relaxation.Conversely, in (b) with a small number of surrounding water molecules, the octahedral structure is maintained.Here (b), the water molecules play a crucial role in stabilizing the Pb-I lattice.

Figure S4 :
Figure S4: Time evolution of the coordination number of N-O, N-I, Pb-N, and Pb-I.

Figure
Figure S4 illustrates the time evolution of the coordination numbers for N-O, N-I, Pb-N, and Pb-I during the initial 8 ps, with cutoff values of 3.5 Å, 4.7 Å, 7 Å, and 3.7 Å, respectively.Notably, within the first 2 ps, substantial changes occurred in all four coordination numbers, indicating significant alterations in the cluster's configuration during this period.Specifically, the coordination number N-O increased from 0.5 to 2.5 within the initial 2 ps,

Figure S5 :
Figure S5: Comparison of the initial and relaxed structures of MAPbI3 clusters.The hydrogen networks and cluster shapes are clearly visualized.The optimized structure shows a slight increase in cluster volume and the incorporation of water molecules, forming a hydrogen bonding network around the clusters.

Table S2 :
The number of water molecules, cosine similarities between the initial and relaxed structures, and band gaps of the naked MAPbI 3 when structure optimized.